The Use of SISO ARX Models in the Determination of the Damage to Dams

Abstract

Modal characteristics of engineering structures can be determined via dynamic observation in scope of system identification and they can be used for a variety of purposes, including model updates, damage assessment, active control, and original design re-evaluation. This paper presents the use of an autoregressive with eXogenous inputs (ARX) model to assess the impact of horizontal displacements in the Oymapinar Dam in Antalya province, Turkey, during the first reservoir filling stage. Besides, displacements in the dam after the filling stage are predicted. There is a high linear correlation between the displacements of the body of the dam and the first filling phase of the reservoir. An ARX model of the dam without damage is created using displacements predicted from a 3D finite element model of the dam and the changes in water level. The displacements in the dam observed in the first filling phase are recalculated using water level changes for damaged or undamaged cases, observed displacements, and the parameters of the undamaged ARX model. The standard deviations of the residuals calculated from the ARX model of the undamaged dam are statistically compared for different confidence intervals using the standard deviations of residuals of the ARX model of the undamaged or damaged dam's observations, and it was determined that there was no dangerous damage to the dam. In addition, the observed displacement values were extended in different scales and standard deviations of these displacements are Downloaded from calculated using the ARX of the undamaged dam model. These standard deviations and the one calculated from undamaged model of the dam were compared, and it was determined that 55 mm of displacement could be dangerous for the dam. Finally, the displacements in the dam for different water levels in the operation phase (after filling) were predicted using the ARX model and were found to be consistent with the measured displacement values.

Online structural damage state identification of concrete arch dams under dynamic loads using a recursive TVARX approach

“…The popular autoregressive with eXogenous (ARX) model is the simplest model incorporating the input signal, and has been one of the most widely used linear dynamic models due to its simple form and easy-to-compute model parameters. Moreover, the model coefficients of the ARX model had a direct correlation with structural stiffness, and combined with advantages such as convenient calculation, fine robustness, and high sensitivity to damage, 35 the ARX model had been one of the popularly employed damage identification methods. The TVARX model was developed from the ARX model, which is often utilized to establish the input–output relationship of a time-variable linear system.…”

Octonion structural response vector and potential structural damage identification method

“…Although the accuracy of vibration mode measurement is less than that of frequency, they are more sensitive to some small local changes in structure (Doebling et al, 1996). Therefore, the methods based on dynamic mode have also attracted much attention in the field of damage detection (Bagchi et al, 2010;Gulal et al, 2011;Hearn et al, 1991;Rezos et al, 1990;Shi et al, 2000;Song et al 1986;West, 1984). Here the vibration mode has a generalized meaning, including mode shape (displacement), modal assurance criteria (MAC), the coordinate MAC (COMAC) and mode shape derivatives such as curvature and strain, etc.…”